Quasi-probability distributions for observables in dynamic systems

2017/02/28 by Patrick P. Hofer
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Distribution (mathematics) #Interference (communication) #Mathematical analysis #Mathematics #Observable #Physics #Probability and statistics #Probability density function #Probability distribution #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Simple (philosophy) #Statistical physics #Statistics #Weak measurement #quant-ph

paper · pdf · doi:10.22331/q-2017-10-12-32

published as Quantum 1, 32 (2017) · Accepted in Quantum

arxiv created 2017/10/11 · openalex publication_date 2017/10/12 · arxiv updated 2017/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.

Citations

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